Well I keep answering my own questions. I found a way to make it work, although it's not the best solution.
I have a hidden .NET textbox on the page which I needed to stay in sync with the datepicker control. This textbox has an id of "datepicker2". So I modified the bottom part of jquery.ui.datepicker.mobile.js to look like this:
I would like to achieve this outside of the constructor, but I could not find any other way to setup an altField and have the datepicker UI update. Maybe this will help other people trying to make this work with .NET though.
I am able to select the date in current month but once I set it using above code and then select a day or switch to next/prev month date picker ui is not proper. It seems that drawMonth and drawYear is resetting the DP and setting it for only selected date only.
See attached screenshots.
using 'jquery.ui.datepicker.mobile.js' library for mobile.